The gravitational force of a star on an orbiting planet 1 is F1. Planet 2, which is three times as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2.?

F_1 / F_2 = 4 / 3

Explanation:

Given:

- Planet 1:-

            mass = m

            orbit = R

- Planet 2:-

           mass = 3m

           orbit = 2R

- Mass of star = M

Find:

- The ratio of gravitational forces F_1 / F_2?

Solution:

- The force of attraction between star and planet 1 is given by:

                                 F_1 = G*(m)*(M) / R^2

- The force of attraction between star and planet 2 is given by:

                                 F_2 = G*(3m)*(M) / (2R)^2

- the ratio of the two forces is:

                                F_1 / F_2 = [G*(m)*(M) / R^2] / [G*(3m)*(M) / (2R)^2 ]

                                F_1 / F_2 = 4 / 3